Optical fibre backscatter polarimetry

ABSTRACT

A method of and apparatus for determining the spatial distribution of polarisation properties of an optical fiber ( 1 ). Pulses ( 7 ) of light are transmitted along the optical fiber ( 1 ) and the polarisation state of light backscattered from portions e and elements R of the optical fiber ( 1 ) detected. A spatial distribution of linear retardance δ, orientation of linear retardance axes q and circular retardance axes can be accurately determined. This has application in the analysis of Polarisation Mode Dispension (PMD) in telecommunications as well as, inter alia, strain, stress, temperature and electric current and voltage measurement using optical fibers.

The present invention relates to optical fibre polarimetry and, inparticular, to a method and apparatus for determining a spatialdistribution of the polarisation properties of a waveguide or opticalfibre.

Knowledge of the polarisation properties of waveguides has various uses.For example, certain polarisation properties of waveguides such asoptical fibres of telecommunications systems, used to transmit signals,can lead to degradation of the transmitted signals. Such signals tend tocomprise very short pulses of light. As the light pulses travel along anoptical fibre, the polarisation state of the light pulses is altered bythe polarisation properties of the optical fibre. This alteration ofpolarisation tends to result in the light pulses becoming less distinctfrom one another and, over large distances, e.g. tens of kilometers, forhigh transmission rate, e.g. 40 Gbit/sec, systems, the light pulses canbecome indistinguishable. This problem is known as Polarisation ModeDispersion (PMD) and is currently considered to be a major factorlimiting the rate at which signals can be transmitted through opticalfibre as well as the length of optical fibres over which signals can besent. Measurement of the polarisation properties of optical fibres istherefore useful in identifying optical fibres or parts of opticalfibres in transmission systems that have high PMD so that they can bereplaced or by-passed for example. Likewise, measurement of thepolarisation properties of optical fibres during or after manufacturecan improve manufacturing processes or quality control for example.

Other reasons that it is useful to determine the polarisation propertiesof optical waveguides arise due to the polarisation properties ofoptical fibre being influenced by external factors. For examples thepolarisation properties of an optical fibre may change when the opticalfibre passes through an electric or magnetic field. Knowledge of thepolarisation properties or changes in polarisation properties of theoptical fibre can therefore enable measurement of the external electricor magnetic field and consequently electric current or voltage.Similarly, polarisation properties of an optical fibre are influenced byphysical forces applied to the optical fibre. For example, stress orstrain such as twisting or bending the optical fibre changes thepolarisation properties of the optical fibre and knowledge of thepolarisation properties of the optical fibre can therefore providemeasurement of the stress or strain. Indeed, it is even possible tomeasure temperature according to changes in the polarisation propertiesof an optical fibre, as the optical fibre can be arranged to experiencestrain under thermal expansion and contraction, for example.

In “Polarisation Optical Time Domain Reflectometry”, Rogers A. J.,Electronics Letters, 19 Jun. 1980, Vol. 16, No. 13, pp 489–490, atechnique for analysing the polarisation properties of optical fibres isdiscussed. This technique is known as Polarisation Optical Time DomainReflectometry (POTDR).

POTDR involves transmitting a pulse of polarised light along an opticalfibre. As the light pulse travels along the optical fibre, some of thelight is scattered by small imperfections and inhomogeneities in theoptical fibre. Such scattering mostly occurs according to Rayleigh'sLaw, i.e. due to imperfections and inhomogeneties that are smaller thanthe wavelength of the light propagating along the optical fibre and thescattering does not, in itself, generally change the polarisation of thelight. Thus, light which is scattered back along the optical fibre tothe end of the optical fibre into which the light pulse was transmitted(backscattered light) has a polarisation state that can be used todeduce information regarding the polarisation properties of the opticalfibre.

The polarisation properties of an optical fibre can be describedcompletely by three quantities: linear retardance δ; orientation of thelinear retardance axes q; and circular retardance ρ. Linear retardance δand orientation of the linear retardance axes q are independent of thedirection in which light travels along the optical fibre, whilstcircular retardance ρ for light travelling in opposite directions alongthe optical fibre is equal and opposite. POTDR only therefore providespartial information regarding the polarisation properties of an opticalfibre. Whilst this has certain applications, the usefulness of POTDR istherefore limited.

In “Computational Polarisation—Optical Time Domain Reflectometry forMeasurement of the Spatial Distribution of PMD in Optical Fibres”,Rogers A. J., Zhou, Y. R., Henderek, U. A., Proc OFMC'97, September1997, pp 126–129, an improvement to POTDR is discussed. This improvedtechnique is known as Computational Polarisation Optical Time DomainReflectometry (CPOTDR).

CPOTDR involves effectively dividing the optical fibre into a series ofadjacent elements starting from an end of the fibre into which lightpulses are transmitted. Each element is considered to have polarisationproperties that are homogeneous, i.e. constant throughout the element,and is effectively further divided into two sections. The polarisationstates of light backscattered in each section of each element isdetermined separately and, from these polarisation states it is possibleto determine the full polarisation properties, i.e. linear retardance δ,orientation of the linear retardance axes q and circular retardance ρ,for each element of the optical fibre in turn.

However, the determination of the polarisation properties of eachelement of an optical fibre by CPOTDR depends on the determinedpolarisation properties of the preceding element, which in turn dependon the determined polarisation properties of the next preceding elementand so on. CPOTDR therefore suffers from accumulation errors. In otherwords, the error in the determined polarisation properties of an elementaffects the determination of the polarisation properties of the nextelement along the optical fibre and so on. This limits the accuracy ofCPOTDR and imposes a limit on the length of optical fibre for whichpolarisation properties can be determined. A limitation also arises inthat the polarisation properties of the optical fibre must be determinedstarting with an element at the end of the optical fibre from which thelight pulses are transmitted into the fibre and then for elements inturn along the optical fibre. It is not possible to start determiningthe polarisation properties of an element of an optical fibre part wayalong the optical fibre until the polarisation properties of allpreceding elements are known. Furthermore, it has not previously beeneasily possible to determine all of the polarisation properties of anoptical fibre, including in particular the orientation of linearretardance axes q.

The present invention seeks to overcome these problems and, according toan aspect of the present invention, there is provided a method ofdetermining a spatial distribution of polarisation properties of anoptical waveguide, the method comprising:

(a) transmitting pulses of polarised light along the optical waveguidefrom an end of the optical waveguide;

(b) detecting a first polarisation state of light emerging from the endof the optical waveguide due to backscattering between the end of theoptical waveguide and an element of the optical waveguide;

(c) detecting a second polarisation state of light emerging from the endof the optical waveguide due to backscattering in a first section of theelement of the optical waveguide;

(d) detecting a third polarisation state of light emerging from the endof the optical waveguide due to backscattering in a second section ofthe element of the optical waveguide;

(e) deducing from the first polarisation state, linear retardance δ_(e)and orientation of linear retardance axes q_(e) of a retarder/rotatorpair equivalent to a portion e of the optical waveguide between the endof the optical waveguide and the element;

(f) determining the polarisation properties of the element from thesecond polarisation state, third polarisation state, deduced linearretardance δ_(e) and deduced orientation of linear retardance axesq_(e); and

(g) repeating steps (a) to (f) for plural elements of the opticalwaveguide to collate a spatial distribution of polarisation propertiesof the optical waveguide,

wherein the determination of polarisation properties of the elementsincludes determination of orientation of linear retardance axes q of theelements by:

repeating (a), (b), (c) and (d) with pulses of light each havingdifferent wavelengths;

deducing values of circular retardance of a retarder/rotator pairequivalent to a portion e of the optical waveguide between the end ofthe optical waveguide and each element minus orientation of the linearretardance axes of the respective element, p_(e) –q, for the pulses oflight having different wavelengths; and

extrapolating the calculated values, p_(e) –q, as p_(e) tends to zerofor increasing wavelength to obtain a value for orientation of thelinear retardance axes q of each element.

According to another aspect of the present invention, there is providedan apparatus for determining a spatial distribution of polarisationproperties of an optical waveguide, the apparatus comprising:

a light source for transmitting pulses of polarised light along theoptical waveguide from an end of the optical waveguide;

a detector for detecting a first polarisation state of light emergingfrom the end of the optical waveguide due to backscattering between theend of the optical waveguide and an element of the optical waveguide, asecond polarisation state of light emerging from the end of the opticalwaveguide due to backscattering in a first section of the element of theoptical waveguide, and a third polarisation state of light emerging fromthe end of the optical waveguide due to backscattering in a secondsection of the element of the optical waveguide; and

a processor for deducing, from the first polarisation state, linearretardance δ_(e) and orientation of linear retardance axes q_(e) of aretarder/rotator pair equivalent to a portion e of the optical waveguidebetween the end of the optical waveguide and the element, determiningthe polarisation properties of the element from the first polarisationstate, second polarisation state, deduced linear retardance δ_(e) anddeduced orientation of linear retardance axes q_(e), controlling thelight source and detector to repeat the transmission and detection forplural elements of the optical waveguide, repeating the deduction anddetermination for the plural elements of the optical waveguide andcollating a spatial distribution of polarisation properties of theoptical waveguide from the determined polarisation properties of theplural elements,

wherein:

the light source transmits pulses of light each having differentwavelengths;

the detector detects the first, second and third polarisation for thepulses of light of different wavelengths; and

the processor deduces values of circular retardance of aretarder/rotator pair equivalent to a portion e of the optical fibrebetween the end of the optical fibre and the element minus orientationof the linear retardance axes of the element, p_(e)–q, for the pulses oflight of each different wavelength and extrapolates the calculatedvalues, p_(e)–q, as p_(e) tends to zero for increasing wavelength toobtain a value for orientation of the linear retardance axes of eachelement.

In other words, the applicant has recognised that the completepolarisation properties of any element of an optical waveguide can bedetermined from these deduced polarisation states of light backscatteredfrom the optical waveguide. More specifically, the linear retardanceδ_(e) and orientation of linear retardance axes q_(e) of the opticalwaveguide between the end of the optical waveguide and the element maybe deduced from only the first polarisation state. Likewise, thepolarisation properties of each element of the optical waveguide may bedetermined from only the second polarisation state, third polarisationstate, deduced linear retardance δ_(e) and deduced orientation of linearretardance axes q_(e) for the respective element.

This enables a spatial distribution of the polarisation properties ofall or part of an optical waveguide to be determined straightforwardlyin comparison to CPOTDR and without significant accumulation errors. Theoverall length of optical waveguide to which the method and apparatus ofthe invention can be successfully applied is therefore significantlygreater than that to which CPOTDR can be successfully applied. Indeed,the length of optical waveguide for which a spatial distribution ofpolarisation properties can be determined is only effectively limited byattenuation of backscattered light in the optical waveguide.

The invention is applicable to various optical waveguides. However, theoptical waveguide may suitably be an optical fibre. In particular, theoptical waveguide may be a mono-mode optical fibre.

The light source may transmit pulses of light having properties suitablefor transmission in the particular optical waveguide underconsideration. Typically, the light of the pulses may be substantiallymonochromatic and coherent. It may be linearly polarised. A typicalwavelength of the light may be around 1550 nm or in the range 1550 nm to1560 nm. It may therefore be convenient for the light source to comprisea laser. A light coupler may be used to direct the transmitted lightinto the optical waveguide.

Complete polarisation properties of the elements of the opticalwaveguide can be determined. For example, the determined polarisationproperties of the elements may include linear retardance δ, orientationof linear retardance axes q and circular retardance ρ. Alternatively,the polarisation properties of the elements or the spatial distributionof polarisation properties of the optical waveguide can be expressed inother forms, such as a matrix or matrices, or graphically. Not all thepolarisation properties of an element need therefore be calculated. Theadvantage of the invention lies in the ability to determine any desiredpolarisation properties of the optical waveguide or an element of theoptical waveguide without accumulation errors.

The determination of polarisation properties of the elements can beadapted to extract the desired polarisation properties in a convenientand efficient manner. For example, by omitting calculations that relateonly to undesired polarisation properties. However, where it is desiredto determine the orientation of linear retardance axes q, it ispreferred that this is achieved by:

repeating (a) to (d) with pulses of light having different wavelengths;

deducing values of circular retardance of the optical waveguide betweenthe end of the optical fibre and each element minus orientation of thelinear retardances axes of the respective element, ρ_(e)−q, for thepulses of light having different wavelengths; and

extrapolating, for each element, the calculated values, ρ_(e)−q as ρ_(e)tends to zero for increasing wavelength to obtain a value fororientation of the linear retardance axes q.

In other words, it is preferred that the light source transmits pulsesof light having different wavelengths;

the detector detects the first, second and third polarisation states forthe pulses of light having different wavelengths; and

the processor deduces values of circular retardance of the opticalwaveguide between the end of the optical waveguide and each elementminus orientation of the linear retardance axes of the respectiveelement, ρ_(e)−q, for the pulses of light having the differentwavelength and extrapolates, for each element, the calculated values,ρ_(e)−q as ρ_(e) tends to zero for increasing wavelength to obtain avalue for orientation of the linear retardance axes q.

The method and apparatus of the invention are convenient as there is nophysical distinction between circular retardance ρ_(e) of the opticalwaveguide between the end of the optical waveguide and each element andorientation of the linear retardance axes q of the respective element.It is therefore more straightforward to extrapolate orientation of thelinear retardances axes q by determining circular retardance of theoptical waveguide between the end of the optical waveguide and eachelement minus orientation of the linear retardance axes of therespective element, ρ_(e)−q, for different wavelengths of light.

The different wavelengths of light of the light pulses may be selectedas desired. Preferably, at least three different wavelengths, or threepulses having different wavelengths of light, are transmitted for eachelement in order to provide accurate extrapolation. In particular,pulses having wavelengths of light varying from 1500 nm to 1560 nm maybe transmitted for each element. The light source may thereforeconveniently comprise a tuneable laser.

The first polarisation state may be that of light emerging from the endof the optical waveguide due to backscattering substantially at an endof the element closest to the end of the optical waveguide into whichthe light pulses are transmitted.

The first and second sections may be substantially adjacent. They may besubstantially equal in length along the major axis of the opticalwaveguide. Indeed, the first and second sections of the element maytogether define the element.

Preferred embodiments of the present invention will now be described, byway of example only, with reference to the accompanying drawings, inwhich:

FIG. 1 is a perspective view of an optical fibre;

FIG. 2 is a longitudinal, sectional view of the optical fibre of FIG. 1;

FIG. 3 is a transverse, sectional view of the optical fibre of FIG. 1;

FIG. 4 is a longitudinal, sectional view of the optical fibreillustrating Polarisation Optical Time Domain Reflectometry;

FIG. 5 is a longitudinal, sectional view of an optical fibreillustrating Computational Polarisation Optical Time DomainReflectometry;

FIG. 6 is a longitudinal, sectional view of an optical fibreillustrating a method of determining the spatial distribution ofpolarisation properties of an optical fibre according to the invention;

FIG. 7 is a graphical illustration of a determination of orientation oflinear retardance axes q according to the invention;

FIG. 8 is a schematic illustration of an apparatus for determining thespatial distribution of polarisation properties of an optical fibreaccording to the invention; and

FIG. 9 is an illustration of an optical fibre arranged for temperaturemeasurement according to the invention.

The invention is applicable to various types of waveguide and inparticular to any optical waveguide that provides mono-mode transmissionof light. Whilst the examples below are described with reference to anoptical fibre, these examples can be extended to application in otheroptical waveguides when applicable.

Referring to FIGS. 1 to 3, an optical fibre 1 is an optical fibrecomprising a core 2, which might be cylindrical and made from silica(i.e. glass) or another highly optically transmissive material, and acladding 3 which generally encloses the circumference of the core 2along the length of the optical waveguide 1. A typical diameter D forthe optical fibre 1 might be 100 μm. The core 2 has a refractive indexn_(cr) and the cladding 3 has a refractive index n_(cl). The refractiveindex n_(cr) of the core 2 is greater than the refractive index n_(cl)of the cladding 3, i.e. n_(cr) >n_(cl), such that light passinggenerally along the length of the core 2 is totally internally reflectedin the core 2 at a boundary 4 between the core 2 and cladding 3.

In this example, the geometry and refractive indices n_(cr) and n_(cl)of the core 2 and cladding 3 are selected such that only one reflectionangle θ at the boundary 4 between the core 2 and cladding 3 results inthe propagation of light of wavelength λ along the optical fibre 1. Morespecifically,

${\frac{\pi\; D}{\lambda}( {n_{cr}^{2} - n_{cr}^{2}} )^{\frac{1}{2}}} \leq 2.405$

Such an optical fibre 1 is said to transmit light of wavelength λ in a“single-mode” or “mono-mode”. This is well known in the art and thefeatures of such fibres will not therefore be described in detail.

One characteristic of such mono-mode propagation of light is that, atany point along the length of the optical fibre 1, light has a singlepolarisation state. In other words, due to the propagationcharacteristics of the optical fibre 1, light passing from one pointalong the length of the optical fibre 1 to another point along thelength of the optical fibre 1 travels substantially the same distance.This has the result that the polarisation state of light at any givenpoint along the optical fibre 1 is singular and definite rather thancomprised of plural polarisation states.

However, the polarisation state of light varies from point to pointalong the length of the optical fibre 1 due to the polarisationproperties of the optical fibre 1. In an ideal optical fibre, the changein polarisation of light as it passes along the fibre might be constant.In practice, the change in polarisation of light as it passes along theoptical fibre 1 varies and is dependent on a number of factors. Inparticular, bends, twists and inhomogeneities in the optical fibre 1 andin particular the shape of the core 2 cause varying changes inpolarisation. External influences, such as stress, magnetic fields,electric fields and radiation, can also affect the change inpolarisation of light passing along the optical fibre 1.

In more detail, light propagates along a mono-mode optical fibre withtwo polarisation modes, which may be thought of as orthogonal ellipses5, 6, for example as illustrated in FIG. 4. Each ellipse 5, 6 iseffectively the locus of points mapped by the electric field vector oflight propagating in the respective mode over a single wavelength of thelight. As light propagates along the mono-mode optical fibre 1, theshape of the ellipses changes due to the polarisation properties of theoptical fibre 1.

One polarisation property exhibited by the optical fibre 1 is linearbirefringence. Linear birefringence may result from, inter alia, thecore 2 not being perfectly circular. In other words, slight ellipticityof the core 2 can result in linear birefringence. Linear birefringencecan be thought of as causing the major axes of the ellipses 5, 6, i.e.the linear polarisation component of each polarisation mode, topropagate at different velocities. This results in the generation of aphase difference between the linear polarisation component of eachpolarisation mode over a given length of the optical fibre 1, whichphase difference is referred to as linear retardance δ. In order tofully define the linear birefringence of the optical fibre 1, it is alsonecessary to consider by how much the major axis of at least one of theellipses 5, 6 or linear polarisation components of the polarisationmodes rotate over a given length of the optical fibre 1 and this isreferred to as the orientation of linear retardance axes q.

Another polarisation characteristic exhibited by the optical fibre 1 iscircular birefringence. Circular birefringence may result from, interalia, axial twists in the core 2. Circular birefringence can be thoughtof as causing the degree of ellipticity of the ellipses 5, 6, i.e. thecircular component of the each polarisation mode, to propagate along theoptical fibre at different velocities. The difference in the velocity ofpropagation of the circular components of each polarisation mode isreferred to as circular retardance ρ.

Linear retardance δ, orientation of the linear retardance axes q andcircular retardance ρ fully define the polarisation properties of agiven length of the optical fibre 1. It is therefore desired to be ableto determine these parameters in order to assess the polarisationproperties of the optical fibre 1.

In the prior art, Polarisation Optical Time Domain Reflectometry (POTDR)has been used with some success to measure the polarisation propertiesof a mono-mode optical fibre. Such a method is described in“Polarisation Optical Time Domain Reflectometry”, Rogers, A. J.,Electronics Letters, 19 Jun. 1980, Vol 16, No. 13, pp 489–490.

Briefly, referring to FIG. 5, a pulse 7 of light is transmitted alongthe optical fibre 1 (in a forward direction) by transmitting the pulse 7of the light into the optical fibre at end 8 of the optical fibre 1. Asthe pulse 7 of light passes along the optical fibre 1 smallimperfections or inhomogeneities in the optical fibre 1 cause the lightto be reflected or scattered according to Rayleigh's Law. Some of thisscattered light returns along the optical fibre 1, emerges from the end8 of the optical fibre 1 and can be detected. Rayleigh scattering doesnot affect the polarization of the light and the light returning alongthe fibre therefore carries information regarding the polarizationcharacteristics of the optical fibre 1 up to the point at which thescattering took place.

Light backscattered at a first axial position A along the optical fibre1 will return to the end 8 of the optical fibre 1 at a first time t₁.Light reflected at a second axial position B along the optical fibre 1will return to the end 8 of the optical fibre 1 at a second, later timet₂. Thus, by analysing the polarization state of light emerging from theend 8 of the optical fibre 1 at the first and second times t₁, t₂,information regarding the polarization properties of the optical fibre 1between the points A and B can be determined.

However, whilst linear birefringence is independent of the direction inwhich light is travelling along the optical fibre 1, circularbirefringence is not. Indeed, circular birefringence in one directionalong the optical fibre 1 is equal and opposite to circularbirefringence in the opposite direction along the optical fibre 1.

Computational Polarization Optical Time Domain Reflectometry (CPOTDR)was developed in order to overcome this limitation. CPOTDR is described,for example, in “Computational Polarization-Optical Time DomainReflectometry for Measurement of the Spatial Distribution of PMD inOptical Fibres”, Rogers A. J., Zhou Y. R. and Henderek V. A., Proc.OFMC'97, September 1997, pp 126–129.

Briefly, referring to FIG. 6, in CPOTDR, the optical fibre 1 isconsidered as a series of elements Z₁ to Z_(i) in FIG. 6, with elementZ₁ being adjacent the end 8 of the optical fibre 1. The elements Z₁ toZ_(i)each have the same axial length along the optical fibre 1 and areadjacent one another. Each element 9 has linear retardance δ_(i),orientation of linear retardance axes q_(i) and circular retardanceρ_(i). Pulses 7 of light are transmitted along the optical fibre 1 (in aforward direction) and the backscattered light analysed in a mannersimilar to POTDR.

In CPOTDR, the elements Z₁ to Z_(i) are effectively divided into twoequal sections 10, 11. The polarisation state of light backscattered ineach section of each element Z₁ to Z_(i) is detected at end 8 of theoptical waveguide 1, as illustrated in FIG. 6. A Jones matrix can beused to describe the polarisation properties of each element Z₁ to Z_(i)of the optical waveguide 1. The change of polarisation of lightpropagating forward and then backscattered through each section 10, 11of each element Z₁ to Z_(i) is determined by the product of the relevantJones matrices. Starting from the end 8 of the optical section 1, thesesuccessive products are shown as:

$\begin{matrix}\begin{matrix}{M_{1}^{T}M_{1}} \\{( {M_{1}M_{1}^{\prime}} )^{T}( {M_{1}M_{1}^{\prime}} )} \\{( {M_{2}M_{1}M_{1}^{\prime}} )^{T}( {M_{2}M_{1}M_{1}^{\prime}} )} \\{( {M_{2}M_{2}^{\prime}M_{1}M_{1}^{\prime}} )^{T}( {M_{2}M_{2}^{\prime}M_{1}M_{1}^{\prime}} )} \\\vdots \\{{( {M_{i}M_{i}^{\prime}\mspace{11mu}\ldots\mspace{14mu} M_{1}M_{1}^{\prime}} )^{T}( {M_{i}M_{i}^{\prime}\mspace{14mu}\ldots\mspace{14mu} M_{1}M_{1}^{\prime}} )} =} \\{M_{1}^{T}M_{1}^{\prime T}\mspace{14mu}\ldots\mspace{14mu} M_{i}^{\prime T}M_{i}^{T}M_{i}M_{i}^{\prime}\mspace{14mu}\ldots\mspace{14mu} M_{1}^{\prime}M_{1}}\end{matrix} & (1)\end{matrix}$

Where M_(i) is the Jones matrix of the first section 10 of each elementZ_(i) and M_(i) ^(T) is its transpose and M_(i)′ is the Jones matrix ofthe second section 11 of each element Z_(i) and M_(i)′^(T) itstranspose. These matrix products can be derived from detection of thepolarisation characteristics of backscattered light emerging from end 8of the optical fibre 1. The Jones matrix for an element Z₁ to Z_(i) withboth linear and circular birefringence has the form:

$M = \begin{pmatrix}{\alpha + {{\mathbb{i}}\;\beta\;{\cos( {2q} )}}} & {{- \gamma} + {{\mathbb{i}}\;\beta\;{\sin( {2q} )}}} \\{\gamma + {{\mathbb{i}}\;\beta\;{\sin( {2q} )}}} & {\alpha - {{\mathbb{i}}\;\beta\;{\cos( {2q} )}}}\end{pmatrix}$

${\alpha = {\cos\mspace{11mu}\Delta}},{\beta = {\frac{\delta}{2}\mspace{11mu}( \frac{\sin\;\Delta}{\Delta} )}},{\gamma = {P\frac{\sin\;\Delta}{\Delta}}}$

with

$\begin{matrix}{\Delta = {{( {\rho^{2} + \frac{\delta^{2}}{4}} )^{\frac{1}{2}}\mspace{14mu}{and}\mspace{14mu}\alpha^{2}} + \beta^{2} + {\gamma^{2}1}}} & (2)\end{matrix}$

The product of the form M^(T) M is equivalent to a linear retarder andhas the general form:

$\quad\begin{pmatrix}{A + {{\mathbb{i}}\; B}} & {{\mathbb{i}}\; C} \\{{\mathbb{i}}\; C} & {A - {{\mathbb{i}}\; B}}\end{pmatrix}$

whereA ² +B ² +C ²⁼1A=α ²+γ²−β²B=2β(α cos(2q)−γ sin(2q))C=2β(α sin(2q)+γ cos(2q))  (3)

In equations (3), we see that there are only two independent equationsfor the three unknowns. However, as mentioned before, each element iseffectively divided into two sections 10, 11. When the product M_(i)^(T)M_(i) for the first section and M_(i)′^(T)M_(i)′ for the secondsection 11 of an element Z_(i) are known, equations (3) show that fourindependent equations are then available for the three parameters δ_(i),q_(i) and ρ_(i). By solving these equations, the Jones matrix of theelement Z_(i) can be found. In other words δ_(i), q_(i) and ρ_(i) can bedetermined.

However, from equations (1) it is seen that only for the first elementZ₁ are the products M₁ ^(T)M₁ and (M₁M₁′)^(T)(M₁M₁′) obtained directly.For the succeeding elements Z_(i), the products for each element Z_(i)are obtained by using the calculated Jones matrices for the precedingelements Z₁ to Z_(i−1). Therefore, the accuracy of the calculatedparameters δ_(i), q_(i) and ρ_(i) depends on the calculation accuracy ofthe parameters for the preceding elements Z₁ to Z_(i−1).

Referring to FIG. 7, in a method of determining the spatial distributionof polarization characteristics of the optical fibre 1 according to theinvention, the optical fibre 1 is considered as a series of discreteelements R in which the polarization properties of the optical fibre 1are considered to be homogeneous. Each element R is, in turn, consideredas two adjacent sections R1, R2 of equal size, although in otherexamples, the elements R may be divided into a different number of othersize sections as desired. The element R is considered to havepolarization characteristics, to be determined, comprising linearretardance δ, orientation of the linear retardance axes q and circularretardance p.

Conveniently, the portion e of the optical fibre 1 can be considered asa retarder-rotator pair. In other words, half of the portion e can beconsidered to have polarization properties comprising only the linearretardance δ_(e) and orientation of the linear retardance axes q_(e) andthe other half of the portion e can be considered to have polarizationproperties comprising only circular retardance ρ_(e). So, the linearretardance δ_(e) of the portion e and the orientation of the linearretardance areas q_(e) of portion e can be deduced directly from thepolarisation state of light backscattered from point C to the end 8 ofthe optical fibre 1.

As for CPOTDR, it is possible to derive the Jones matrix products M_(R1)^(T)M_(R1) and M_(R2) ^(T)M_(R2) from detection of the polarisationslate of backscattered light emerging from the end of the opticalwaveguide 1. Equations (3) therefore show that we from M_(R1) ^(T)M_(R1)and M_(R2) ^(T)M_(R2) have four independent equations for the fourparameters δ, q, ρ and ρ_(e). By solving these equations, the Jonesmatrix M_(R) of element R and δ, q and p can be found.

However, there is no physical distinction between circular retardanceρ_(e) and orientation of the linear retardance axes q, and Q=(ρ_(e)−q)is the parameter that is directly calculable, although, in otherexamples, (ρ_(e)+q) might be calculated. Circular retardance ρ_(e)depends on the wavelength λ of light, whilst orientation of the linearretardance axes q does not. Furthermore, circular retardance ρ_(e)(λ)decreases to zero as wavelength λ increases to infinity. Referring toFIG. 8, it is therefore possible to calculate Q(λ) for light pulses ofdifferent wavelengths λ and extrapolate a value for orientation of thelinear retardance axes q.

Referring to FIG. 9, an apparatus 100 for determining the spatialdistribution of polarisation properties of an optical fibre comprises alight source 12, which, in this example, is a tunable laser able totransmit polarised, coherent light of any desired wavelength between1550 nm and 1560 nm. Light transmitted by the light source 12 isdirected into a beamsplitter 13. The beamsplitter 13 transmits some ofthe light incident on it from the light source 12 to an optical coupler14, in this example by admitting the light to pass straight through thebeam splitter 13. Some of the light incident from the light source 12 isalso transmitted to a polarisation analyser 15, in this example byreflecting the light through an angle of 90°.

The optical coupler 14 passes light incident on it from the beamsplitter13 into the optical fibre 1 through the end 8 of the optical fibre 1.The optical coupler 14 also transmits light emitted from the end 8 ofthe optical fibre 1, for example by backscattering in the optical fibre1, to the beamsplitter 13. This emitted, e.g. backscattered, light isre-directed by the beamsplitter 13 to the polarisation analyser 15.

The polarisation analyser 15 comprises a Stokes analyser. Morespecifically, the polarisation analyser 15 has four optical elementsarranged in the path of the light re-directed from the beamsplitter 13.The optical elements comprise, in series, a first linear polariser, asecond linear polariser arranged at 45° to the first linear polariser, aquarter wave plate, i.e. an optical element that retards light byquarter of a wavelength, and a third linear polariser arranged at thesame orientation as the second linear polariser. Light emerging fromeach of the linear polarisers is incident on a photodetector 16, such asphotodiode array. Thus, the intensity of the light of each polarisationstate separated by the linear polarisers is detected by thephotodetector 16.

The intensity information is output by the photodetector 16 to aprocessor 17, such as the Central Processing Unit (CPU) of a PersonalComputer (PC). The processor 17 is able to formulate the output of thephotodetector 16 in the Stokes Formalism which represents thepolarisation state of light emitted from the end 8 of the optical fibre1. The Stokes Formalism allows a Mueller matrix of the general form:

$M_{r =}\begin{pmatrix}1 & 0 & 0 & 0 \\0 & {A_{R}^{2} + B_{R}^{2} - C_{R}^{2}} & {2B_{R}C_{R}} & {{- 2}A_{R}C_{R}} \\0 & {2B_{R}C_{R}} & {A_{R}^{2} + C_{R}^{2} - B_{R}^{2}} & {2A_{R}B_{R}} \\0 & {2A_{R}C_{R}} & {{- 2}A_{R}B_{R}} & {{- A_{R}^{2}} - B_{R}^{2} - C_{R}^{2}}\end{pmatrix}$

It is possible to determine the Jones matrices and linear retardance δorientation of linear retardance axes q and circular retardance ρ fromthe Mueller matrices of light backscattered in the optical fibre 1 asset out above.

The processor 17 is connected to a light source controller 18 forcontrolling the light source 12. The light source controller 18 isoperable to select the wavelength at which light is transmitted by thelight source 12 and the light pulse 7 timing and duration. The timingand duration of the light pulses 7 transmitted by the light source 12can be verified by the processor 17 from the output of the photodetector16 corresponding to light transmitted from the beamsplitter 13 to thepolarisation analyser 15 from light incident on the beamsplitter 13 fromthe light source 12.

The timing and duration of the pulses 7 of light emitted by the lightsource 12 controlled, in combination with the time at which the outputof the photodetector 16 is analysed, to resolve light backscattered inappropriate parts of the optical fibre 1, as described above. Thus,different elements R of the optical fibre 1 can be resolved.

The output of the processor 17 is transmitted to an output device 19which, in this example, is a display such as an oscilloscope or otherCathode Ray Tube (CRT) monitor. The output is indicative of thedetermined polarisation properties at the optical fibre 1.

In a first example, the apparatus 100 is adapted to measure PolarisationMode Dispersion in a telecommunications system. The optical coupler 14is adapted to transmit light into telecommunications optical fibres fortesting, either in situ or during or after manufacture. The output isindicative of a spatial distribution of PMD along the fibre on test andenables fibres or part of fibres having anomalously large PMD to beidentified and, e.g., discarded.

In a second example, referring to FIG. 10, the optical fibre 1 is woundinto a uniform helix. The strain along the length of the optical fibre 1is therefore substantially uniform. The apparatus 100 is adapted tomeasure the spatial distribution of polarisation properties of theoptical fibre 1 from time to time. The change in the distribution ofpolarisation properties of the optical fibre 1 is indicative of changesin strain in respective parts of the fibre which, in turn, is indicativeof changes in temperature at those parts causing thermal expansion orcontraction of the optical fibre. Thus, after calibration, the apparatus100 is able to output a spatial distribution of temperature along thelength of the optical fibre 1.

Changes in bending of the optical fibre 1 generally cause changes inlinear retardance δ and orientation of linear retardances axes q.Changes in twisting of the optical fibre 1 generally cause changes incircular retardance ρ. In another example, the apparatus 100 thereforecorrelates linear retardance δ and orientation of linear retardance axesq with circular retardance to provide a more accurate spatialdistribution of temperature along the length of the optical fibre 1.

In “Optical-Fibre Current Measurement”, Rogers, A. J., Optical-FibreSensing Technology, Chapman and Hall (Edited by Grattan and Meggitt)1995, Chapter 13B pp 421–440, a method of measuring current flowingthrough a loop of optical fibre is described. In another example of theinvention, the apparatus 100 is adapted to improve this technique.

In this example, the optical fibre 1 is formed in a loop with anelectric current to be measured passing axially through the loop. Thisarrangement results in the magnetic field generated by the electriccurrent passing along the loop of optical fibre 1 axially. This inducesa non-reciprocal circular retardance ρ in the optical fibre 1 by theFaraday magneto-optic effect.

Measurement of circular retardance ρ therefore provides a measurement ofcurrent. However, in the prior art, vibrationally-induced linearretardance δ and orientation of linear retardances axes q interfere withmeasurement of circular retardance ρ. The spatial distribution ofpolarisation properties output by the apparatus 100 can separate linearretardance δ and orientation of linear retardance axes q from circularretardance ρ and a more accurate measurement of current is thereforeproduced.

In yet another example, the optical fibre 1 is arranged such that anelectric field induces a linear birefringence in this optical fibre 1.The apparatus 100 determines a spatial distribution of the polarisationproperties of the optical fibre 1 that is indicative of the electricfield acting on the fibre. Integration of the electric field between twopoints along the fibre yields a measurement of voltage between the twopoints. Vibrational effects can be discriminated against by knowledge ofthe electric field direction(s) or frequency discrimination. Incombination with the example set out above, both electric current andelectric voltage can be measured by apparatus 100.

In another example, the optical fibre 1 is arranged to undergo the samestrain as a structure, the strain on which it is desired to measure. Forexample, the optical fibre 1 may be embedded in a reinforced concreteslab of a building or bridge. As strain on the optical fibre 1 changesthe spatial distribution of polarisation properties of the optical fibre1, measured by apparatus 100, changes. Thus, a spatial distribution ofthe strain or stress on the structure can be determined.

1. A method of determining a spatial distribution of polarisationproperties of an optical waveguide, the method comprising: (a)transmitting pulses of polarised light along the optical waveguide froman end of the optical waveguide; (b) detecting a first polarisationstate of light emerging from the end of the optical waveguide due tobackscattering in the optical waveguide between the end of the opticalwaveguide and an element of the optical waveguide; (c) detecting asecond polarisation state of light that emerges from the end of theoptical waveguide due to backscattering in a first section of theelement of the optical waveguide; (d) detecting a third polarisationstate of light that emerges from the end of the optical waveguide due tobackscattering in a second section of the element of the opticalwaveguide; (e) deducing, from the first polarisation state, linearretardance δ_(e) and orientation of linear retardance axes q_(e) of aretarder/rotator pair equivalent to a portion e of the optical waveguidebetween end of the optical waveguide and the element; (f) determiningthe polarisation properties of the element from the second polarisationstate, third polarisation state, deduced linear retardance δ_(e) anddeduced orientation of linear retardance axes q_(e); and (g) repeatingsteps (a) to (f) for plural elements of the optical waveguide to collatea spatial distribution of polarisation properties of the opticalwaveguide, wherein the determination of polarisation properties of theelements includes determination of orientation of linear retardance axesof the elements by: repeating (a), (b), (c) and (d) with pulses of lighteach having different wavelengths; deducing values of circularretardance of a retarder/rotator pair equivalent to a portion e of theoptical waveguide between the end of the optical waveguide and eachelement minus orientation of the linear retardance axes of therespective element, p_(e)–q, for the pulses of light having differentwavelengths; and extrapolating the calculated values, p_(e)–q, as p_(e)tends to zero for increasing wavelength to obtain a value fororientation of the linear retardance axes q of each element.
 2. Themethod of claim 1, wherein the determined polarisation properties of theelements include linear retardance δ, orientation of linear retardanceaxes q and circular retardance ρ of the elements.
 3. The method of claim1, wherein the optical waveguide is an optical fibre.
 4. The method ofclaim 1, wherein the optical waveguide is a mono-mode optical fibre. 5.The method of claim 1, wherein the first detected polarisation state isthat of light backscattered substantially at the end of the elementclosest to the end of the optical waveguide.
 6. The method of claim 1,wherein the first and second sections of the element are substantiallyadjacent.
 7. The method of claim 1, wherein the first and secondsections of the element are substantially equal in length along themajor axis of the optical waveguide.
 8. The method of claim 1, whereinthe first and second sections of the element together define theelement.
 9. An apparatus for determining a spatial distribution ofpolarisation properties of an optical waveguide, the apparatuscomprising: a light source for transmitting pulses of polarised lightalong the optical waveguide from an end of the optical waveguide; adetector for detecting a first polarisation state of light emerging fromthe end of the optical waveguide due to backscattering in the opticalwaveguide between the end of the optical waveguide and an element of theoptical waveguide, a second polarisation state of light that emergesfrom the end of the optical waveguide due to backscattering in a firstsection of the element of the optical waveguide, and a thirdpolarisation state of light that emerges from the end of the opticalwaveguide due to backscattering in a second section of the element ofthe optical waveguide; and a processor for deducing, from the firstpolarisation state, linear retardance δ^(e) and orientation of linearretardance axes q_(e) of a retarder/rotator pair equivalent to a portione of the optical waveguide between end of the optical waveguide and theelement, determining the polarisation properties of the element from thefirst polarisation state, second polarisation state, deduced linearretardance δ_(e) and deduced orientation of linear retardance axesq_(e), controlling the light source and detector to repeat thetransmission and detection for plural elements of the optical waveguide,repeating the deduction and determination for the plural elements of theoptical waveguide and collating a spatial distribution of polarisationproperties of the optical waveguide, wherein: the light source transmitspulses of light each having different wavelengths; the detector detectsthe first, second and third polarisation for the pulses of light ofdifferent wavelengths; and the processor deduces values of circularretardance of a retarder/rotator pair equivalent to a portion e of theoptical fibre between the end of the optical fibre and the element minusorientation of the linear retardance axes of the element, p_(e) –q, forthe pulses of light of each different wavelength and extrapolates thecalculated values, p_(e) –q, as p_(e) tends to zero for increasingwavelength to obtain a value for orientation of the linear retardanceaxes q of each element.
 10. A method of determining Polarisation ModeDispersion (PMD) in an optical fibre comprising the method of claim 1.11. An apparatus for determining Polarisation Mode Dispersion in anoptical fibre comprising the apparatus of claim
 9. 12. A method ofdetermining changes in the polarisation properties of an optical fibredue to external influences, the method comprising the method of claim 1.13. An apparatus for determining changes in the polarisation propertiesof an optical fibre due to external influences, the apparatus comprisingthe apparatus of claim
 9. 14. Computer software adapted to carry out themethod of claim
 1. 15. The method of claim 2, wherein the opticalwaveguide is a mono-mode optical fibre.
 16. The method of claim 2,wherein the optical waveguide is a mono-mode optical fibre.
 17. Computersoftware adapted to carry out the method of claim
 10. 18. Computersoftware adapted to carry out the method of claim 12.